A conventional oil pump apparatus of this kind is disclosed, for example, in Japanese Utility-Model Laid-Open Publication No. 1-125806 and Japanese Utility-Model Laid-Open Publication No. 4-006510. The oil pump include a regulator valve mechanism which regulates the pressure of oil discharged from a discharge port to portions of an engine. In general, the oil pump apparatus is mounted at the front side of the engine and it is necessary to avoid an interference with a timing chain or an oil pump driving chain and so on when the oil pump is mounted. In such circumstance, the oil pump apparatus disclosed in the former publication has the regulator valve mechanism which is disposed on a body and which is projected outward from the body so as to avoid the interference with the timing chain. Therefore, the side of the oil pump is increased and the oil pump takes up lots of space for mounting on the engine. In the later publication, the regulator valve mechanism is disposed in a discharge passage of an engine block for avoiding the interference with the chain. In this oil pump, however, it is necessary to form ribs for preventing the generation of in order to achieve the foregoing object, the present invention provides an oil pump apparatus which includes a body, a first rotor and a second rotor disposed in the body so as to be able to rotate and a regulator valve mechanism for regulating the pressure of oil discharged to portions of an engine, wherein the regulator valve mechanism is disposed in the inside of the body and the engine and includes a regulator valve member which moves in the direction being in parallel with a rotation axis of the first and second rotors in response to the discharged oil pressure.